Optimization of recursive cascade filters

The optimum design of recursive digital filters in the cascade realization with respect to the output noise is healed here by taking into account the ordering, the pole-zero pairing, and the selection of configurations of the individual sections. In the first part of this paper, the output noise variances are derived for arbitrary realized cascaded configuration employing either the fixed-point or the floating-point arithmetics. The second part presents a simple algorithm to compute the output noise variance without direct evalution of complex integral. An example is presented in which the individual sections are allowed to take on different configurations.